If N, C, and D are positive integers, what is the remainder

No, it is not.

Take some simple numbers: 11 divided by 5 gives quotient as 2 and remainder as 1.

\(\frac{11}{5} \neq 2 + 1\)

So \(\frac{(ND+NC)}{CN} \neq Q + 5\)

Actually, ND + NC = Q*CN + 5

OA is definitely wrong. Should be E.
you cannot write remainder(ND/NC) = remainder(D/C)

eg remainder(20/15) = 5, remainder(4/3) = 1

I agree. Let me expand this out to show the actual cases that prove insufficiency.

(1)
case 1: D = 19, C = 14. Obeys the statement, because when 20 is divided by 15, the remainder is 5. The answer to the question is also 5.
case 2: D = 28, C = 5. Obeys, the statement, because when 29 is divided by 6, the remainder is 5. The answer to the question, though, is 3. That's because when you divide 28 by 5, the remainder is 3.

(2)
case 1: D = 4, C = 3, N = 5. Obeys the statement, because when 20 + 15 is divided by 15, the remainder is 5. The answer to the question is 1.
case 2: D = 20, C = 15, N = 1. Obeys the statement, because when 20+15 is divided by 15, the remainder is 5. The answer to the question, however, is 5.

We have two different possible answers to the question for statement 1, and two different possible answers for statement 2. Now let's put them together.

(1+2)
case 1: D = 19, C = 14, N = 1.
- Obeys statement 1 (we already tested it).
- It also obeys statement 2, because when 19 + 14 is divided by 14, the remainder is 5.
- The answer to the question is 5.

case 2: D = 25, C = 6, N = 5.
- Obeys statement 1: 26 divided by 7 has a remainder of 5.
- Obeys statement 2: 125 divided by 30 has a remainder of 5.
- The answer to the question is 1.

So, the answer is (E).

That said, on the test, I would work on this one for about 90 seconds and then guess either C or E.

1. insufficient b/c D and C can be any number. adding +1 can change remainder completely.
ex: D =2 , C = 3 R = 2 ... D = 2+1 , C = 3+1 R = 3
2: sufficient b/c (ND + NC)/CN => ND/CN + NC/CN => ND/CN =>D/C + 1 => R5

answer: B

Can someone please help with a detailed explanation? Was able to get the answer right but don't really know how I arrived at it.

Thanks

Well, I am confused here and need some help.

I chose D.

Reason is as follows:
For statement A:
take D+1=12 and C+1=7 so 12/7 => remainder 5
if we take 11/6 => remainder is still 5

In the explanation above for D=CK + (K + 4), for different values of K, we are actually changing the value of D while keeping the value of C same. If the algebra calculations are correct and logic is correct, there must be some example to support this explanation.

We all agree to sufficiency of statement B.

Please advise.

Sorry to bother , I just want to ask ... N can't be 5 ? 5/N will still be integer i.e. 1
Could you please explain why only value N can take is 1?

Actually it can take value 5 too. I will rewrite the solution given above soon.

In statement 1, say if C+1 = 8 and D+1 = 21, remainder is 5.
C = 7 and D = 20, remainder is 6.
Not sufficient alone.

1- Statement 1 insuf, C and D could be lot of number possibilities
2- N(D+C)/CN = D+C/C = D/C +1 = Q + 5/C => D = QC +4 is this good ?

I don't understand how you got Q + 5/C from Q*CN + 5.

N,C,D are positive integers.
d/c =quotient + rem. We need to find remainder.

1) D+1/C +1 = 0 + 5
--> D = 9, C = 2. 7+1/3 = 0+ 5. D/C =9/2 = remainder = 1
--> D = 10+1, C = 5+1 --> 11/6 = 0 +5 = D/C = 10/ 2 --> no remainder

So NS

2) (ND + NC)/ NC = q + 5 --> ND +1 = q + 5 -->ND = 4. what is D and N?

1) 2) --> still no value to C,D,N. So E

Hi

I believe that even without plugging numbers we can identify two equations from given statements using simply Dividend (N) = Divisor (D) * Quotient (Q) + Remainder (R)

St 1 - (C+1)x + 5 ;
St 2 - (CN)x + 5

Since there is no information about C nor N despite combination, the variables may or may not generate common values to consider, thus making insufficient to answer.